Introduction and Applicability of Nonlinear Principal Components Analysis

Abstract

Nonlinear principal component analysis (NLPCA) is a descriptive dimension reduction method that examines the relationships between variables and displays the results numerically and visually in multivariate datasets that have a linear or nonlinear relationship between them. In this study, it was aimed to present the basic explanatory information about nonlinear principal components analysis (NLPCA) and to emphasize its usability by performing application. In the study, data obtained from 270 samples for 17 continuous variables concerning 3 pepper varieties were evaluated by Principal components analysis (PCA). With the 4 principal components obtained as a result of PCA, being 3 categorical variables Variety, storage time and Application were analyzed by NLPCA. In the analysis made with PCA, approximately 74% of the total variance was explained and in the analysis made with NLPCA, approximately 58% was explained as well. As a result of the analysis; it was observed that there was a strong relationship between PC1 and storage time and variety, and PC3 and PC2 variables, while the relationship between PC4 and application variables and all variables was low. As a result; by examining the linear and nonlinear relationships between the variables in the multivariate datasets, these relationships intended to be presented in an easily interpreted and easily understandable way in two-dimensional space; it was emphasized that NLPCA can be used alone and/or together with other multivariate analysis methods.